How do I apply for a long term visa or obtain a Z type in my case?

Patrick, she can't hire you. In order to find a job to work legally, you should find a corp. that is capable of hiring foreigners. Not all Chinese companies or individuals can hire a foreigner. After you find your employer. He/she will help you acquire the work permit first. Then you need to use this permit to apply for Z type.

If you plan to stay with her for long, then you both might consider getting married. After you get married, then you can apply Q1 type, which enables you to stay for long. However, you can't work under Q1 type.